Drag the tiles to the correct boxes to complete the pairs. match the functions to their x-intercepts.
1) f(x)= log x-1
2) f(x)= -(log x-2)
3) f(x)= log (-x-2)
4) f(x)= -log -(x-1)
a) (0,0)
b) (-3,0)
c) (10,0)
d) (100,0)

See below in bold.

Step-by-step explanation:

The x intercepts occur when f(x) = 0.

1.  logx  - 1 = 0

logx = 1

By the definition of a log ( to the base 10):

x  = 10^1 = 10

So the x-intercept is  c (10,0).

2. - (logx - 2) = 0

logx - 2 = 0

log x = 2

so x = 100.

So it is d (100,0).

3 .   log(-x - 2)  = 0

-x - 2 = 10^0 = 1

-x = 3

x = -3

So it is  b (-3, 0).

4.  f(x) = -log -(x - 1)

log - (x - 1) = 0

log 1 = 0

so -(x - 1) = 1

- x + 1 = 1

x = 1-1 = 0

So  it is a. (0,0).

     Function                               x-intercept

We know that the x-intercept of a function is the point where the function value is zero.

i.e. the x where f(x)=0

1)

when we have:

Hence, taking the exponential function on both the sides of the equation we have:

The x-intercept is: (10,0)

2)

when,

we have:

Since,

Hence, we have:

Taking anti logarithm on both side we get:

Hence, the x-intercept is:

(100,0)

3)

when

we have:

On taking anti logarithm on both the side of the equation we get:

Hence, the x-intercept is: (-3,0)

4)

when,

Hence, the x-intercept is:  (0,0)

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